Note that \(\mu _{-1}(C_o)=C_o\)  and our computations in Magma [1]} show that the fixed subcode of \(C_o\)  under the action of multiplier \(\mu _{-1}\)  has the minimum distance 37. Hence \(d(C_o)\ge 19.5\)  by Proposition \(\ref {fix-subcode order 2}\)  and the inequality \(d \ge d(C_o)+1\)  implies that \(d\ge 20.5\) . The fact that \(d\)  is even shows that \(Q\)  has parameters \([[182,0,d\ge 22]]\) . Thus \(Q\)  is a new quantum code; the previous best known quantum code had minimum distance 21.
